IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 1 An event-triggered receding-horizon scheme for planning rail operations in maritime terminals Claudia Caballini, Cecilia Pasquale, Simona Sacone, Member, IEEE, Silvia Siri, Member, IEEE Abstract—This paper proposes a planning approach to op- timize railway operations in seaport terminals by adopting a queue-based discrete-time model of the considered system. Firstly, a mixed-integer linear mathematical programming prob- lem is defined in order to optimize the timing of import trains and the use of the handling resources devoted to rail port operations. Secondly, in order to deal with unexpected situations or uncertainty in estimating some data necessary to the planning, an event-triggered receding-horizon planning approach is proposed in which the finite horizon optimization problem is solved whenever a critical event happens or the real values of some problem data significantly differ from the predicted ones. Both these planning approaches are tested on data referred to a real terminal and deeply discussed in the paper. Index Terms—Seaport container terminals; rail operations; optimization; receding-horizon planning. I. I NTRODUCTION C ONTAINER terminals are very complex systems with highly dynamic interactions among the various han- dling, transportation, and storage units and are affected by incomplete knowledge about future events, both in terms of data accuracy and correctness and in terms of timing of information arrival [1]. Different simulation, optimization and control approaches have been developed by researchers for planning terminal operations, as shown for instance in [2], [3]. The planning techniques and the models adopted can be classified according to different decision levels, i.e. terminal design, operative planning, and real-time control [1] or they can be classified according to the specific process they address, as done in [4], [5]. In these two latter surveys, in particular, optimization methods can be distinguished among those re- ferred to ship planning processes, those related to storage and stacking logistics, those devoted to transport optimization and simulation-based techniques. This work is devoted to model the rail port cycle in a seaport terminal and to define a planning approach in order to optimize the timing of the different processes involved (preliminary versions can be found in [6] and [7]). The dynamic model adopted is quite aggregate and represents the movement of containers in the railway area of the terminal as a set of flows; the presence of containers in a specific zone of the terminal is modelled as a queue and the queue dynamics is given by conservation discrete-time equations. The movement of containers is represented as a transfer between queues. Such model takes inspiration from [8] in which the whole seaport The authors are with the Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genova, Via Opera Pia 13, 16145 – Genova, Italy. container terminal is modeled by a system of queues and the proposed optimization problem aims at defining the optimal utilization of terminal resources in order to minimize the trans- fer delays of containers. More in detail, in [8] the queue model represents the entire terminal at a very aggregate level and the resulting planning problem is linear and characterized by continuous variables (indicating flows of containers). Instead, this work focuses specifically on the rail port cycle and models it more in detail; in fact, some “binary” decisions have to be taken and then the resulting planning problem has a mixed- integer linear structure. Moreover, in this paper we propose an event-triggered receding-horizon approach for planning the operations, whereas in [8] a standard receding-horizon scheme is adopted. A similar model, again on the entire terminal, can be found in [9] where two feedback control strategies for the allocation of terminal resources are proposed and compared through sensitivity and scenario analyses. Whereas the models and optimization approaches present in the literature and devoted to specific terminal processes are manifold, few works address the planning of the ter- minal by adopting aggregate models. For instance, in [10] a mathematical model is developed to optimize import and export processes in a seaport terminal assuming that many aspects (such as loading/unloading plans, container locations, and so on) have been already planned. The overall view of the terminal is also considered in many works adopting discrete simulation, which can be considered as an effective and challenging alternative approach for container terminal analysis [11]. In [12] a microscopic simulation model is developed for evaluating four different automated container terminal concepts in terms of performance and costs. In [13] a discrete-event simulation model is adopted to study inland terminals for combined rail/road transport, whereas in [14] an object-oriented model to be used in a port decision support sys- tem is proposed. In [15] queueing network-based models are adopted to optimally manage the container discharge/loading at any given berthing point via discrete-event simulation. The modelling tool of Petri nets is used in [16] in order to evaluate the impact of Information and Communication Technologies in the connection between a port and a truck terminal. As already mentioned, the queue-based discrete-time model considered in this paper addresses the processes associated with the import rail cycle, starting from the storage of con- tainers, going through their loading on trains, till the shunting operations of trains and their exit from the terminal through the electric line. Some papers can be found in the literature referred to rail operations in container terminals, more often inland than maritime terminals, generally with a different focus